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Alice’s take-home pay last year was the same each month, and she saved

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Alice’s take-home pay last year was the same each month, and she saved [#permalink] New post 06 Sep 2005, 20:01
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Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?

A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/6

OPEN DISCUSSION OF THIS QUESTION IS HERE: alice-s-take-home-pay-last-year-was-the-same-each-month-and-91893.html
[Reveal] Spoiler: OA
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Re: Alice’s take-home pay last year was the same each month, and she saved [#permalink] New post 06 Sep 2005, 22:56
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Alice's take-home pay was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?


solution:

Suppose the portion of her salary that she saved is X
and the remaining portion is Y

X+Y= total take home salary

given, 12X = 3Y

or 4X = Y

Total take-home salary= X+ 4X= 5X

hence, she saved 1/5-th portion of her take home salary
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Re: Alice’s take-home pay last year was the same each month, and she saved [#permalink] New post 21 Mar 2015, 06:40
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Re: Alice’s take-home pay last year was the same each month, and she saved [#permalink] New post 21 Mar 2015, 07:57
Expert's post
coffeeloverfreak wrote:
Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?

A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/6

OPEN DISCUSSION OF THIS QUESTION IS HERE: alice-s-take-home-pay-last-year-was-the-same-each-month-and-91893.html


Let Alice's monthly take-home pay be \(p\) and her monthly savings be \(s\). Total savings will be \(12s\) and we know that this is 3 times the amount she spends in month which is: \(p-s\). So we have:

\(12s=3(p-s)\) --> \(s=p\frac{1}{5}\)

Answer: D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: alice-s-take-home-pay-last-year-was-the-same-each-month-and-91893.html
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Re: Alice’s take-home pay last year was the same each month, and she saved   [#permalink] 21 Mar 2015, 07:57
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